On the smoothness of convex envelopes

Griewank, A.; Rabier, P. J.

doi:10.1090/S0002-9947-1990-0986024-2

On the smoothness of convex envelopes

Authors: A. Griewank and P. J. Rabier
Journal: Trans. Amer. Math. Soc. 322 (1990), 691-709
MSC: Primary 49J52; Secondary 90C30
DOI: https://doi.org/10.1090/S0002-9947-1990-0986024-2
MathSciNet review: 986024
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Abstract: We examine differentiability properties of the convex envelope $\operatorname{conv} E$ of a given function $E:{{\mathbf{R}}^n} \to ( - \infty ,\infty ]$ in terms of properties of . It is shown that ${C^1}$ as well as optimal ${C^{1,\alpha }}$ regularity results, $0 < \alpha \leqslant 1$ , can be obtained under general conditions.

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